Question: If we express $x^2 - 5x$ in the form $a(x - h)^2 + k$, then what is $k$?
We complete the square.  We can square $x - \frac{5}{2}$ to get $x^2 - 5x + \frac{25}{4}$, so $x^2 - 5x = \left( x - \frac{5}{2} \right)^2 - \frac{25}{4}$.  We see that $k = \boxed{-\frac{25}{4}}$.